Sorry, I'm not sure I completely understand what your saying. I know cyano is primarily photoautorophic and can fix CO2 and nitrogen, however, it is often capable of various modes, including heterotrophy, or at least mixed photoheterotropy. So, I'm pretty certain it can metabolize organic carbon So, it may not need organic carbon, but why wouldn't it benefit from it?
It might use some as other photosynthetic organisms do.
I personally don't know of any documented heterotrophic modes for cyano but would be interested in learning about them if you or others have information to share.
Just don't see why it would metabolize much if any C . At least not to the degree heterotrophic bacteria will. The heterotrophs when provided an organic carbon source will compete for phosphate and nitrogen depriving the cyano of it which should offset any benefit cyano may or may not get from the extra C.
I raised the same argument you make several years ago but have since favored bacterial by products as a more likely explanation in some carbon dosing applications where cyano pops up.
There are many strains of cyano and I'm sure much is unknown about how they operate in our tanks but I can say ,fwiw. that after over 2 years of daily dosing vodka and vinegar ,there is no visible cyano in the heavily fed system except a small patch where some chaeto in one fuge is waning and likely feeding it.If the cyano benefits from the organic C dosing , the gallons of vodka and vinegar I've dosed haven't shown it . Before carbon dosing moderate amounts of visible cyano was a frequent visitor to certain areas in the system.
I doubt it would need to metabolize as much C as a purely heterotrophic bacteria, when in autotrophic mode. However, I'd guess C could still drive it's growth. Also, I'd think mutualism with bacterial populations, would likely also drive a lot of cyano growth when carbon dosing. So, either way, I think there are plausible biological hypotheses for why carbon dosing could drive cyano. And I don't think these hypotheses would necessarily be mutually exclusive.
One good paper is Mannan and Pakrasi 1993. "Dark Heterotrophic Growth Conditions Result in an Increase in the Content of Photosystem II Units in the Filamentous Cyanobacterium Anabaena variabilis ATCC 29413"
I know there are others, IIRC, even some more recent genome studies looking at heterotrophic ability of cyano strains. It's been a while though, so I don't have them handy, but this should point towards some.
As for Mannan and Pakrasi, they looked at the cyanobacteria Anabaena variabilis ATCC 2941 and found it could grow in dark heterotrophic conditions, just as efficiently as in photoautotrophic conditions. There were some cellular changes, such as a change in PSI to PSII ratio, however, it maintained its ability to photosynthesize even after months of darkness.
So, I could hypothesize, that maybe carbon dosing could drive cyano bacteria growth in the shaded areas of the tank. Also, I would think it's growth in this situation, could still likely be enhanced by its mutualistic relationship with heteratrophic bacteria, so, this would help it survive the low nutrient levels. So this may make it very tough to eliminate. People may siphon out cyano where they see it, but who is siphoning their overflows for example? And that cyano, then may be fully capable of moving back to the display and regaining it autotrophic capabilities as conditions allow.
Of course I'm speculating, but it seems fairly plausible based on what I know anyways. One thing I don't know is exactly what types of cyano are found in our aquariums and what their specific capabilities are. It's interesting though, if cyano wasn't such a pest, I think I would really be more fascinated by it. It has to be one of the most adaptive organisms on the planet

For us though, as a result, it's a serious PITA :lol: